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Consecutive cubes and squares


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#1 BMAD

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Posted 27 May 2013 - 12:00 AM

Show that if the difference of the cubes of two consecutive integers is the square of an integer, then this integer is the sum of the squares of two consecutive integers.
 
(The smallest non-trivial example is: 83 − 73 = 169.  This is the square of an integer, namely 13, which can be expressed as 22 + 32.)

 


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#2 DeGe

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Posted 16 July 2013 - 10:49 AM

Spoiler for A start

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#3 superprismatic

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Posted 17 July 2013 - 08:37 PM

Spoiler for some helpful info, perhaps


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